Normally heard as a Mega-Kill Announcer status in Unreal Tournament 2004, Defence of The Ancients and Defence of The Ancients 2. It generally means that a certain player has got more than 9 kills in a row and is making an impressive kill-streak.
The announcement will normally come with the announcer saying "Holy Shit!" in slow motion, and a message on the screen along the lines of " is BEYOND GODLIKE! Someone KILL HIM!!"
This message usually indicates that the indicated player is almost impossible to kill one-on-one and needs to be killed by a team effort, or gang-killing (ganking). Needless to say, it has a demoralising effect on his/her opponents and the reward for killing/fragging such a player is also significantly high.
Kill Announcer: "Holy Shit!" PlayerName (Drow Ranger) is BEYOND GODLIKE! Someone KILL HIM!!
Player on opposing team: Fffffffffuuuuuuuu.............
Another Player on opposing team: This one is GG (Game Gone)
(That's just a sample of a typical reaction to that kind of scenario)
A champion whose level of skill at an activity is so much above that of the common mortal, that mortals aren't really any competition for him. They might as well be facing god, because they're never going to win a single bout.
The term started being popularized by the game Unreal Tournament where the voice of the announcer shouts: GODLIKE! For all to listen, when a player kills 25 enemy players in a row, without dying. This feature was later added to other popular games, DotA-like games being of the most prominent.
Interesting Fact: In DotA you only have to kill 10 players in a row to get Godlike'd. If you kill more than 10 in a row, the DotA announcer says: HOLY SHIT! and adds a subtitle: 'Player is beyond Godlike. PLEASE, somebody kill him!'.
/* A player just killed the entire enemy team while all his teammates were down */
Mortal #1: Did we all just lose against this one guy?
Mortal #1: WTF just happened?
Mortal #2: Hello there,... are you god?
/* Unreal tournament voice: GODLIKE! */